The heavy part of the US military operation in Afghanistan must now be considered pretty much over. The fall of the Taliban's first and last stronghold in Kandahar has left the battle in the Tora Bora mountains to complete the campaign.

That could still be messy, but the dire warnings about the risks of military intervention have so far been mostly proved wrong. In response to the global reach of international terrorism, the US has convincingly displayed the global reach of high-technology firepower, against a hopelessly inferior adversary in one of the world's remotest battlefields. It has all happened much faster than anybody expected in the early stages of the offensive.

The declared aims, of course, have evolved in the process. The overthrow and replacement of the Taliban was not an explicit objective at the start. Both the US and Britain talked of pressuring the regime. Washington's first stated purpose was to "make it clear to the Taliban leaders and their supporters that harbouring terrorists is unacceptable and carries a price".

The Taliban's spectacular collapse in the second half of the campaign has enabled the US to achieve at least one part of its mission - to make an example that may deter some other countries from supporting terrorists - and to set about completing its operation against al-Qaeda's leadership.

Seizing the chance of bringing this operation to an early conclusion, the US has concentrated on its priority tasks, not wanting other considerations such as protection of humanitarian aid to interfere with them.

Rather against expectations, the campaign has met the requirements of modern US doctrine - the application of overwhelmingly superior force, the maintainance of public support and the possibility of a clean exit.

It will probably go down as the clearest success for air power since the Gulf war inaugurated the age of high-precision air strikes a decade ago. Despite some glaring mishaps, advances in guidance and sensor technology enabled the US to achieve greater accuracy with fewer unintended consequences and at longer range than the campaigns in Iraq and former Yugoslavia.

The strikes have proved that co-ordinated air power, even if still not enough on its own to inflict a defeat, can dominate and decide a conflict. This became apparent from the end of October, when intensified attacks began to be mainly directed in support of the northern alliance. Air strikes reversed the military map of Afghanistan's internal conflict, both by the display of US engagement and by sheer destructive power.

They also made it possible for the US to limit the involvement of its own troops. Its preparedness to accept casualties has hardly had to be tested. Its reliance on proxy forces was taken to an extreme when it left to others the responsibility for non-Afghan prisoners captured after the siege of Konduz, with bloody consequences. The question now arises of how to deal with hundreds of foreign fighters in Kandahar.

The setting-up of a Marine Corps base demonstrated US readiness to send in more troops if necessary. But the US seemed more prepared to let the fighting drag on than to become directly involved in a ground assault.

The surprise of the conflict was the ease with which Taliban resistence gave way. The fall of Mazar-e-Sharif on November 10 set a pattern of precipitate retreat repeated a few days later in Kabul. Most observers expected the Taliban to hold at least part of the country until early next year at least. Having crassly overplayed their hand, the Taliban lost more through bloodless desertion than though defeat in battle. Not only did Taliban resilience prove illusory but so - again against predictions - did Osama bin Laden's hopes of provoking a revolt in the Muslim world in response to the US intervention.

Whatever the fate of Mullah Mohammad Omar, the Taliban will have lost all its political and probably military clout, at least for the time being. And whether Osama bin Laden is caught, killed or put to flight, al-Qaeda will have lost much of its effectiveness and potency as an organisation. But - dead, captive or a fugitive - he is likely to remain a hero and a symbol for many people. Having made its point militarily, the US has yet to win the political campaign over what constitutes "unacceptable" behaviour.